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http://dx.doi.org/10.5351/KJAS.2013.26.3.431

A Parameter Estimation Method using Nonlinear Least Squares  

Oh, Suna (Department of Statistics, Ewha Woman University)
Song, Jongwoo (Department of Statistics, Ewha Woman University)
Publication Information
The Korean Journal of Applied Statistics / v.26, no.3, 2013 , pp. 431-440 More about this Journal
Abstract
We consider the problem of estimating the parameters of heavy tailed distributions. In general, maximum likelihood estimation(MLE) is the most preferred method of parameter estimation because it has good properties such as asymptotic consistency, normality and efficiency. However, MLE is not always the best solution because MLE is unstable or does not exist in some cases. This paper proposes another parameter estimation method, non-linear least squares(NLS) and compares its performance to MLE. The NLS estimator is achieved by minimizing sum of squared difference between empirical cumulative distribution function(CDF) and a theoretical distribution function. In this article, we compare the NLS method to MLE using simulated data from heavy tailed distributions. The NLS method is shown to perform better than MLE in Burr distribution when the sample size is small; in addition, it performs well in a Frechet distribution.
Keywords
Parameter estimation; MLE; NLS;
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